An endospore is a dormant, tough, and non-reproductive structure produced by certain bacteria from the Firmicute phylum. The name endospore is suggestive of a spore or seed-like form (endo means within), but it is not a true spore (i.e., not an offspring). It is a stripped-down, dormant form to which the bacterium can reduce itself.
An arithmetic sequence is a linear function. Instead of y=mx+b, we write a n =dn+c where d is the common difference and c is a constant (not the first term of the sequence, however). A recursive definition, since each term is found by adding the common difference to the previous term is a k+1 =a k +d. For any term in the sequence, we've added the difference one less time than the number of the term. For example, for the first term, we haven't added the difference at all (0 times).
Point being, you must include the starting number in any recursive definition. 1  1) An initial condition that tells where the sequence starts. 2  2) A recursion formula that tells how any term of the sequence relates to the preceding term.  Sample of a recursive defintion: 19, 14, 9, 4, .